A friend of a friend is ... a dense network

December 01, 2016

It's a familiar request in the digital age: one of your friends on social media has a friend who wants to be your friend. Frequent linking among friends of friends can cause a rapid increase in social network connectivity.

A new theoretical model shows that networks evolve very differently depending on how often these "second neighbor" connections occur. The work could offer a better understanding of how dense networks form.

Networks--like those based on social media or internet connections--are often characterized by their degree, which is the number of links per member, or node. Previous models of networks have tended to focus on sparse networks in which the degree remains finite as a network grows.

By including friend-of-friend interactions in their model, Renaud Lambiotte (University of Namur, Belgium), Paul Krapivsky (Boston University), and Uttam Bhat and Sid Redner (both Santa Fe Institute) could control the link density of the network.

"It's an incredibly simple model that can produce both sparse and dense networks," says Redner, a Santa Fe Institute professor.

In their recent paper published in Physical Review Letters, the researchers constructed a general network evolution in which every new node links to one target node already in the network, as well as to each of the neighbors of the target (that is, friends of friends), with copying probability p. The likelihood of each of these "copying" steps turns out to be the crucial factor in how the network evolves.

If copying is unlikely, the network evolves into a sparse, skeleton-like framework. But when the copying probability is greater than 1/2, the network becomes dense, with the number of links growing faster than the network itself. This "densifying" behavior has been observed in real world data, such as research paper citation lists, internet router maps, and other networks.

The researchers also investigated multiple-node connections, such as triangles that consist of three mutually-linked nodes. They found that the triangle count grew faster than the network for a copying probability greater than 2/3. In fact, they discovered an unlimited number of these growth transitions related to copying.

"It's kind of exotic, but cool, that such a generic model has all these transitions in it," Redner says.

If similar transitions are identified as real networks evolve--like those in social media--the model's copying mechanism could be an allegory for many real friend-of-friend interactions. The model may also offer a way to study the role of triangles and other so-called "cliques" as information or diseases spread in a population.

Santa Fe Institute

Related Social Media Articles from Brightsurf:

it's not if, but how people use social media that impacts their well-being
New research from UBC Okanagan indicates what's most important for overall happiness is how a person uses social media.

Social media postings linked to hate crimes
A new paper in the Journal of the European Economic Association, published by Oxford University Press, explores the connection between social media and hate crimes.

How Steak-umm became a social media phenomenon during the pandemic
A new study outlines how a brand of frozen meat products took social media by storm - and what other brands can learn from the phenomenon.

COVID-19: Social media users more likely to believe false information
A new study led by researchers at McGill University finds that people who get their news from social media are more likely to have misperceptions about COVID-19.

Stemming the spread of misinformation on social media
New research reported in the journal Psychological Science finds that priming people to think about accuracy could make them more discerning in what they subsequently share on social media.

Looking for better customer engagement value? Be more strategic on social media
According to a new study from the University of Vaasa and University of Cyprus, the mere use of social media alone does not generate customer value, but rather, the connections and interactions between the firm and its customers -- as well as among customers themselves -- can be used strategically for resource transformation and exchanges between the interacting parties.

Exploring the use of 'stretchable' words in social media
An investigation of Twitter messages reveals new insights and tools for studying how people use stretched words, such as 'duuuuude,' 'heyyyyy,' or 'noooooooo.' Tyler Gray and colleagues at the University of Vermont in Burlington present these findings in the open-access journal PLOS ONE on May 27, 2020.

How social media platforms can contribute to dehumanizing people
A recent analysis of discourse on Facebook highlights how social media can be used to dehumanize entire groups of people.

Social media influencers could encourage adolescents to follow social distancing guidelines
Public health bodies should consider incentivizing social media influencers to encourage adolescents to follow social distancing guidelines, say researchers.

Social grooming factors influencing social media civility on COVID-19
A new study analyzing tweets about COVID-19 found that users with larger social networks tend to use fewer uncivil remarks when they have more positive responses from others.

Read More: Social Media News and Social Media Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.